Question

If the universal constant of gravitation $\left(G\right)$ were decreasing uniformly with time, then a satellite in orbit would still maintain its

• A. radius
• B. tangential speed
• C. angular momentum
• D. period of revolution

Answer 1

The correct option is C angular momentum

If the universal constant of gravitation (G) were decreasing uniformly with time, then a satellite in orbit would not maintain its total centripetal force because its only source is gravity, changing G will change that.
$f_c\propto \frac{v^2}{r}-eqn\left(1\right)$
also there is no force or variation of force along it tangential direction and the torque provided by centripetal force is always Zero and hence there will be no change its angular momentum.
i.e., $mvr=constant$ , m is already constant so (v*r) has to be constant.
from above and eqn(1) , conditions we konwIf the universal constant of gravitation (G) were decreasing uniformly with time, then a satellite in orbit would not be able maintain its radius and tangential velocity and hence its period of revolution(depends on $r$ and $v$.)